Related papers: Density of mechanisms within the flexibility windo…
Theoretical studies on the experimental feasibility of hypothetical Zeolitic Imidazolate Frameworks (ZIF) have focused so far on relative energy of various polymorphs, by energy minimization at the quantum chemical level. We present here a…
Results of a series of molecular dynamics simulations of cubic siliceous zeolites suggest that pressure-induced softening -- the phenomenon in which a material becomes progressively more compressible under pressure -- is likely to be a…
The computational discovery and design of zeolites is a crucial part of the chemical industry. Finding highly accurate while computationally feasible protocol for identification of hypothetical zeolites that could be targeted experimentally…
Flexible mechanical metamaterials possess repeating structural motifs that imbue them with novel, exciting properties including programmability, anomalous elastic moduli and nonlinear and robust response. We address such structures via…
A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…
We extend the mathematical theory of rigidity of frameworks (graphs embedded in $d$-dimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes…
In complex crystals close to melting or at finite temperatures, different types of defects are ubiquitous and their role becomes relevant in the mechanical response of these solids. Conventional elasticity theory fails to provide a…
We consider substitution tilings and Delone sets without the assumption of finite local complexity (FLC). We first give a sufficient condition for tiling dynamical systems to be uniquely ergodic and a formula for the measure of cylinder…
In mathematical crystallography and computational materials science, it is important to infer flexibility properties of framework materials from their geometric representation. We study combinatorial, geometric and kinematic properties for…
Soft colloids are increasingly used as model systems to address fundamental issues such as crystallisation and the glass and jamming transitions. Among the available classes of soft colloids, microgels are emerging as the gold standard.…
In a recent publication we established an analogy between the free energy of a hard sphere system and the energy of an elastic network [1]. This result enables one to study the free energy landscape of hard spheres, in particular to define…
The whole compositional range (Ge$_f$ = Ge/(Ge+Si)= 0 to 1) of zeolite STW has been synthesized and studied by a comprehensive combined experimental--theoretical approach. The yield of zeolite goes through a maximum and then drops at the…
Nonlinearities and instabilities in mechanical structures have shown great promise for embedding advanced functionalities. However, simulating structures subject to nonlinearities can be challenging due to the complexity of their behavior,…
A framework, which is a (possibly infinite) graph with a realization of its vertices in the plane, is called flexible if it can be continuously deformed while preserving the edge lengths. We focus on flexibility of frameworks in which…
Glass is a microscopically disordered, solid form of matter that results when a fluid is cooled or compressed in such a fashion that it does not crystallise. Almost all types of materials are capable of glass formation -- polymers, metal…
An analysis of the dynamics is performed, of exactly solvable models for fragile and strong glasses, exploiting the partitioning of the free energy landscape in inherent structures. The results are compared with the exact solution of the…
The dynamical properties and mechanical functions of amorphous materials are governed by their microscopic structures, particularly the elasticity of the interaction networks, which is generally complicated by structural heterogeneity. This…
Soft-granular media, such as dense emulsions, foams or tissues, exhibit either fluid- or solid-like properties depending on the applied external stresses. Whereas bulk rheology of such materials has been thoroughly investigated, the…
The zeolitic imidazolate frameworks (ZIF) have emerged as a promising candidate for catalysis, carbon-dioxide (CO$_{2}$) capture and storage as well as flue gas separation due to their tunable porosity and chemical stability. ZIFs consists…
An introduction and survey is given of some recent work on the infinitesimal dynamics of \textit{crystal frameworks}, that is, of translationally periodic discrete bond-node structures in $\mathbb{R}^d$, for $ d=2,3,...$. We discuss the…